BOSTON – The Massachusetts House on Wednesday unanimously approved a bill designed to soften the impact of new federal flood insurance rules on many of the state’s coastal homeowners.

The measure, sponsored by Democratic House Speaker Robert DeLeo, would tie the level of flood insurance that must be purchased to a homeowner’s outstanding mortgage balance, rather than the full replacement value of the home.

It also would prohibit mortgage lenders from requiring coverage for the contents of a home or including a deductible of less than $5,000.

Lawmakers representing coastal districts said constituents were facing the threat of dramatic increases in flood insurance premiums as a result of new federal regulations.

“This bill is going to help people stay in their homes,” said Rep. James Cantwell, D-Marshfield.

Congress in 2012 approved a law that included a redrawing of the Federal Emergency Management Agency’s flood zone maps and the elimination of federal subsidies, in an effort to keep the National Flood Insurance Program solvent after claims from Hurricane Katrina in 2005.

The program is $24 billion in the red, officials said, mostly because of huge losses from Katrina and Hurricane Sandy.

Rep. Josh Cutler, D-Duxbury, said the new maps issued last year by FEMA added more homes to the flood zone and changed the flood elevation levels for many homeowners. He said concerns were immediately raised about the accuracy of the maps, including what he said was the use of wave calculations from California instead of the East Coast.

“This bill is in effect a circuit breaker to prevent homeowners from being forced literally underwater by federal flood insurance regulations,” Cutler said.

While the bill, which now goes to the Senate, passed the House without opposition, concerns have been raised that the measure would leave some homeowners underinsured in the event of a catastrophic flood.

Attorney General Martha Coakley, who worked with lawmakers in crafting the measure, said in a statement that homeowners would retain the option of buying additional insurance, and noted that the legislation includes a requirement that consumers be notified in writing that their insurance premiums may not be enough to pay for all repairs or property losses.

Tying mandatory insurance coverage to the outstanding mortgage balance, rather than full replacement value, would soften the blow for homeowners, Coakley said.

Federal lawmakers also appear to be responding to pressure to ease the requirements after complaints about sharp increases in premiums.

The U.S. Senate has backed a measure calling for a four-year delay in implementation of the law, and the U.S. House approved a bill that would allow sellers to give their subsidized, below-market insurance rates to new buyers and lower the cap on how much flood insurance premiums can rise each year.